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On the market impact of wind energy forecasts

Jónsson, Tryggvi; Pinson, Pierre; Madsen, Henrik

Published in:Energy Economics

Link to article, DOI:10.1016/j.eneco.2009.10.018

Publication date:2010

Document VersionEarly version, also known as pre-print

Link back to DTU Orbit

Citation (APA):Jónsson, T., Pinson, P., & Madsen, H. (2010). On the market impact of wind energy forecasts. EnergyEconomics, 32(2), 313-320. https://doi.org/10.1016/j.eneco.2009.10.018

On the market impact of wind energy forecasts

Tryggvi Jonsson∗,a,b, Pierre Pinsona, Henrik Madsena

aDTU Informatics, Technical University of Denmark, Richard Petersens Plads,

building 321, DK-2800 Kgs. Lyngby, DenmarkbENFOR A/S, Lyngsø Alle 3, DK-2970 Hørsholm, Denmark

Abstract

This paper presents an analysis of how day-ahead electricity spot prices

are affected by day-ahead wind power forecasts. Demonstration of this

relationship is given as a test case for the Western Danish price area of

the Nord Pool’s Elspot market. Impact on the average price behaviour

is investigated as well as that on the distributional properties of the

price. By using a non-parametric regression model to assess the effects

of wind power forecasts on the average behaviour, the non-linearities

and time variations in the relationship are captured well and the ef-

fects are shown to be quite substantial. Furthermore, by evaluating the

distributional properties of the spot prices under different scenarios, the

impact of the wind power forecasts on the price distribution is proved to

be considerable. The conditional price distribution is moreover shown

to be non-Gaussian. This implies that forecasting models for electric-

ity spot prices for which parameters are estimated by a least squares

techniques will not have Gaussian residuals. Hence the widespread

assumption of Gaussian residuals from electricity spot price models is

shown to be inadequate for these model types. The revealed effects are

likely to be observable and qualitatively similar in other day-ahead elec-

tricity markets significantly penetrated by wind power.

Key words: Electricity market, Spot prices, Wind power forecasts,

Locally weighted polynomial regression, Conditional distributions

∗Corresponding author

Email addresses: trjo@imm.dtu.dk/tj@enfor.dk (Tryggvi Jonsson),

pp@imm.dtu.dk (Pierre Pinson), hm@imm.dtu.dk (Henrik Madsen)

Preprint submitted to Working Paper October 23, 2009

1. Introduction

Since the beginning of the nineties, electricity markets around the

world have undergone drastic reforms, resulting in a more deregulated

structure. The backbone of these changes has been the adoption of

wholesale electricity markets, in which producers and distributors bid

for purchase and sale of electricity. Commonly, these bids are placed

through a central clearing mechanism which determines a spot price

at which electricity is traded. However due to the complex nature of

the commodity in question, the dynamics of these spot prices are only

partially understood, making them difficult to accurately forecast. Nev-

ertheless, understanding of the price dynamics (and the resulting in-

creased predictability) is paramount for all market participants and

regulators, for the purpose of planning, trading, risk management or

alternatively market design (see e.g. Daneshi and Daneshi, 2008).

The complex nature of spot prices arises from numerous causes.

First of all, anti-gaming policies along with the instantaneous nature

of electricity and restrictions on its transmission make arbitrage over

time and space nearly impossible (Boogert and Dupont, 2005; Sewalt

and de Jong, 2003). Secondly, demand for electricity, seen from a short-

term perspective, is highly inelastic and has distinctive and complex

characteristics in the first two moments, (see e.g. Taylor and McSharry,

2007 or Panagiotelis and Smith, 2008 and references therein). Thirdly,

the electricity supply function is discontinuous, convex and steeply in-

creasing at the high demand end (Nord Pool Spot AS, 2006a; Karakat-

sani and Bunn, 2008). In parallel, the presence of non-dispatchable

renewable energy sources causes frequent variations in the shape of

the supply function, due to their low marginal costs and potential pri-

oritisation (Giabardo and Zugno, 2008). In addition, market design is

generally complex and frequently changing support schemes for some

plant technologies often lead to modifications of the market design as

well. Finally, the oligopolistic structure in many markets has given rise

to a debate about to what extent market power is exercised. Although

controversial, evidence of market power being put to force has been doc-

umented on many major electricity markets (see e.g. Eggertsson, 2003;

Schwarz et al., 2007; Christensen et al., 2007 and also Karakatsani and

Bunn, 2008 for other sources). A main objective of the present paper is

to demonstrate that wind power forecasts have an impact on the mar-

ket, and to describe how they quantitatively affect prices on the elec-

tricity market.

2

The combination of all the factors listed above results in a price be-

haviour unlike what is observed for most other traded commodities as

the price time-series often exhibits periodicity, inter- and intra-day cor-

relations, trends, mean reverting spikes, positive skewness and heavy

tails (see e.g. Conejo et al., 2005; Panagiotelis and Smith, 2008; Kosater

and Mosler, 2006, for empirical evidence of this). Furthermore, the in-

creased emphasis on renewable energy sources around the world has

made the dynamics of spot prices even more complex. The price char-

acteristics have become more extreme and made prices even harder to

predict - partly due to the very volatile nature of many of these energy

sources.

Several papers have been dedicated to describing the short-term dy-

namics of electricity spot prices, either by (i) relying solely on previ-

ous values, i.e. in a univariate time-series modelling framework (Huis-

man et al., 2006; Conejo et al., 2005; Cuaresma et al., 2004), (ii) by

accounting for the price’s response to demand, fuel prices or weather

conditions (Vehvilainen and Pyykkonen, 2005; Ruibal and Mazumdar,

2008; Mandal et al., 2006; Nogales and Conejo, 2006), or (iii) by us-

ing regime-switching approaches (Kosater and Mosler, 2006; Gonzalez

et al., 2005). However as correctly stated by Karakatsani and Bunn

(2008), the models presented in those papers have a number of limita-

tions. Firstly, fuel prices and weather conditions only affect the supply

function indirectly and their influence on the elements of the supply

function is highly non-linear. Therefore, those factors ought to be sup-

plemented by, or transformed into, information that more directly af-

fects the supply function and the behaviour of market participants in

general, as suggested by Karakatsani and Bunn (2008) and Longstaff

and Wang (2004). Secondly, most research works have been focused

on daily averages or baseload/peakload averages which conceal to some

or full extent the distinct intra-day variations of the prices. Recently,

higher frequency analysis have appeared though (e.g. Huisman et al.,

2006; Longstaff and Wang, 2004; Karakatsani and Bunn, 2008).

Operationally, energy produced by non-dispatchable energy sources

is commonly bid into the markets using forecasts of the future produc-

tion. In the case of wind power, production forecasting is a major and

rapidly growing research field and has been the topic of countless pa-

pers (see e.g Giebel et al., 2003; Costa et al., 2008, for a state of the

art review). Some efforts have been made to optimise the bidding of

wind energy into deregulated electricity markets based on these fore-

casts, and in some cases on information about their situation-dependent

3

uncertainty as well (Pinson et al., 2007; Matevosyan and Soder, 2006;

Bathurst et al., 2002). These studies however have all regarded wind

power as a price taker, and therefore not considered its potential effects

on prices. Although this approach is suitable when concentrating on in-

dividual wind power generators, wind power as a whole is in fact a price

maker as originally suggested by Skytte (1999) and Morthorst (2003),

due to its extremely low marginal cost. In areas where wind power has a

significant share in the generation portfolio, the most substantial short-

term changes in the global supply function arise from variations in wind

power generation. As shown by Giabardo et al. (2009), estimated future

wind power generation1 appears as a stochastic threshold in the sup-

ply function. The present paper presents an analysis of how electric-

ity spot prices, for the case of the Western Danish price area (DK-1) of

Nord Pool’s Elspot market, are affected by wind power forecasts. The

analysis puts emphasis on the effects of such forecasts on the mean be-

haviour of the prices, on the intra-day variations of these effects, as well

as on the corresponding impact on the distributional characteristics of

day-ahead electricity prices. Some studies have been presented on the

effects of actual power generated by wind turbines on the spot prices

in the area (Skytte, 1999; Morthorst, 2003; Moesgaard and Morthorst,

2008; Enevoldson et al., 2006) and they have shown this effect to exist

— as also expected by economical arguments. However, these studies

have been bounded to linear effects on the mean behaviour and have

therefore neither captured the full extent of this impact nor any of the

distributional effects. Furthermore, as the analysis are carried out on

the actual measured power output they only show the presence of a

relation between wind power generation and spot prices, rather than

proving wind power to be a price maker on the market. Consequently,

the resulting models can not be used for forecasting.

Showing wind power as a price maker in a short-term perspective,

implies raising the question: “What will the electricity spot prices be, if it

is believed that the wind will/will not blow?” As an answer to this ques-

tion, the relationship between wind power forecasts and spot prices is

shown not only to exist, but also to be highly non-linear and time de-

pendent. Furthermore, it is demonstrated that the correlation between

demand and wind power forecasts should not be neglected since it is

1And thereby wind power capacity due to the low marginal costs and sometimes

prioritisation of wind power

4

in fact the ratio between the forecasted wind power generation and the

forecasted load that has the strongest association with the spot prices.

In parallel, this proportional contribution of wind power to the supply

is shown to have substantial influence on the distribution of the spot

prices as well.

For the demonstration of these effects, a non-parametric regression

model is employed. The relationship between forecasted wind power

production and electricity spot prices is estimated for every hour of the

day. This dependency is estimated by assuming that the relationship

can be locally described with a second order polynomial. For estima-

tion, a least squares criteria is employed allowing for the mean effect

of forecasted wind power penetration on the prices to be extracted. De-

spite the facts listed about the (non-Gaussian) properties of the condi-

tional spot price distribution, this approach serves well for estimating

the mean behaviour of the spot prices, partially due to the non-linear

properties of the model and the large amount of data used as input to

analysis. Employing such a criteria for the non-parametric regression

model prevents however from any inference on the effects of wind power

forecasts on distributional properties of spot prices to be made. There-

fore, the evaluation of these effects is performed by directly analysing

the first four moments of the price distributions under different scenar-

ios of the ratio between forecasted wind power and forecasted load. The

wind power forecasts used are generated by WPPT2 (see Nielsen et al.,

2002), a wind power forecasting tool that has been successfully used in

Denmark over the past years and was used for bidding aid by almost

every wind turbine owner in DK-1 during the period in question.

The remainder of the paper is structured as follows: Section 2 de-

scribes the market structure at Elspot and the data set used as input to

the analysis. Section 3 provides a brief introduction to the mathemati-

cal approach to the modelling. In Section 4, an analysis of how the mean

behaviour of the spot prices is affected by wind power forecasts is given,

while the impact of these forecasts on the price distribution is the topic

of Section 5. Finally, concluding remarks are given in Section 6 along

with some general discussion.

2The Wind Power Prediction Tool

5

2. Nord Pool’s Elspot

2.1. Market Setting

The analysis presented in this paper is done on data from the West-

ern Danish price area (DK-1) of Nord Pool’s Elspot market. Elspot is a

day-ahead physical delivery market for electricity. It is currently oper-

ating in the entire Scandinavia (Denmark, Finland, Norway and Swe-

den) and in the so called Kontek area, located in Northeastern Germany.

At Elspot, spot prices are set by a market equilibrium model, where

supply and demand curves of all market participants are matched on a

day-ahead basis. Gate closure is at noon each day for the period mid-

night to midnight in the following day and prices are published later

in the day with a resolution of one hour. The one hour prices are cal-

culated by matching the collaborative supply and demand curves, cal-

culated from the bids and ask prices placed by the market participants

(see Nord Pool Spot AS, 2006a,b, for details). This price, found from bids

from all market participants, defines the system price from which the

area prices are defined.

Due to transmission constraints, the region covered by Elspot is di-

vided into several price areas. Physical constraints on transmission de-

fine the outer bounds of each price area, implying that transmission

capacity within an area can be regarded as unlimited. The area spot

prices are calculated in the same manner as the system price, but only

considering the bids within the area along with possible utilisation of

the transmission lines to surrounding areas (see Nord Pool Spot AS,

2006b, for details). The area prices, which determine at what price

physical trading is done within an area, can therefore differ quite con-

siderably between areas. If none of the interconnections between areas

are fully utilised, the system price is valid in the whole region. However,

this is seldom the case and therefore is modelling of the area spot prices

appropriate when short term dynamics and forecasting are considered.

The DK-1 price area consists of Jutland, Funen and the islands west

of the Great Belt. The area is an interesting context for investigation

of electricity spot prices as it can be said to represent the future of

liberalised electricity markets. This is because it has relatively large

connections to its surrounding areas, and is heavily penetrated by an

inexpensive, non-dispatchable energy source, i.e. wind power. In fact,

DK-1 is currently the grid area in the world that has the largest share of

wind power in its generation portfolio, with more than 20% of its annual

consumption generated by wind turbines.

6

2.2. The Data

The data, which the analysis here presented is carried out on, covers

the period from January 4th 2006 to October 31st 2007. It consists of

hourly area spot prices along with hourly consumption measurements

for the area3 and wind power forecasts (in MW) with a temporal reso-

lution of 15 minutes, made at 07:00 on the day before delivery for lead

times up to 48 hours. The forecasts are made using WPPT (see Nielsen

et al., 2002).

If the analysis is to be true to the criteria of analysing future elec-

tricity prices, both measures entering the wind power-load ratio have

to be forecasts instead of actual measurements. When load forecasts

are made using state of the art load forecasting models (e.g. Taylor and

McSharry, 2007), the relationship between the actual load and the pre-

dicted load can be described as

Lt = Lt + εt where εt ∼ N(0,σ2) (1)

where Lt is the actual load, Lt is the predicted load and σ2 is the fi-

nite variance of the residuals, εt. Hence, by adding a Gaussian noise

with the appropriate variance to the load measurements, a time series

that has the characteristics of an actual load forecast series is obtained.

The standard deviation of the noise is chosen as 2% of the average load

for the period, since it reflects the performance of state of the art load

forecasting models (see e.g. Taylor and McSharry, 2007). The use of

simulated load forecasts gives rise to some deviations from the real-

life situation though. First of all, the residuals of actual load forecasts

are bound to have some autocorrelation in the lags up to the prediction

horizon. This is not reflected in the simulated residuals. However, for

forecasts of such a degree of accuracy as load forecasts are in general,

the small prediction error is reflected by a small residual autocorrela-

tion as well. The influence of the missing autocorrelation structure is

therefore only marginal. Secondly, since both load forecasts and wind

power predictions are typically based on weather forecasts, some cor-

relation between the errors of the two might be observed in practise.

This is however not the case when simulated forecasts are used since

the computer generated noise, added to the load forecasts, is not corre-

lated to the real error of the wind power predictions. The error of the

3Available at http://www.energinet.dk/en/menu/Market/Market.htm and

at http://www.nordpoolspot.com

7

wind-load forecasting ratio will therefore have characteristics that dif-

fer slightly from what would be observed if both were actual forecasts.

Nevertheless, the mean of the errors will still be zero in both cases and

other effects are minor. These potential dissimilarities from the prac-

tical situation are ignored in the analysis to follow due to their small

impact on the results.

Hourly wind energy forecasts in MWh also have to be derived. This

is done by linearly interpolating between each two adjacent forecasts in

every hour and taking the result as the production in MWh for that 15

minute period. These interpolations are then summed up for each hour.

So in mathematical terms, an hourly forecast is obtained by

V(h)t =

5

∑i=2

0.25 ·

V

(q)t,q(i−1)

+ V(q)t,q(i)

2

(2)

where V(h)t (hereafter noted as Vt) is the hourly wind energy forecast

for hour t, and V(q)t,q(i)

is the 15 minute wind power forecast for quarter i

within hour t.In order to account for the correlation between demand and wind

power forecasts, the wind power penetration level, V(p)t , is defined as

V(p)t =

Vt

Lt

, (3)

Finally, it should be emphasised that no extreme events are excluded

from the data set.

3. Non-parametric regression modelling of day-ahead electric-

ity prices

The relationship between, area spot price and wind power genera-

tion is far from being linear. It is therefore essential for obtaining a

proper estimate of the effects of wind power forecasts on the area spot

price to account for these non-linearities. The problem of estimating a

complex non-linear relationship between variables is however not a triv-

ial one. But by assuming that the relationship is locally linear or locally

describable by a low order polynomial the problem is much more con-

venient to deal with. One could locally solve a weighted least squares

problem as described in detail for the general case in (Cleveland and

Devlin, 1988; Nielsen et al., 2000; Madsen and Holst, 2000).

8

Let a model for the spot prices at time t, Pt, be defined as

Pt = θ(xt) + εt, (4)

where θ(·) is a vector of coefficient functions and εt is a noise term.

Furthermore, xt is a vector of explanatory variables. In this case those

variables are some direct or derived form of a wind power forecast, Vt,

and an hour of the day indicator, kt.

The functions θ(·) are estimated at a number of distinct points by

approximating the functions using polynomials and fitting the resulting

linear model locally to each of these fitting points. More specifically, let

U =[

VU kU

]Tdenote a particular fitting point, chosen from a set of

m total fitting points, and let p2(U) be a column vector of terms in the

corresponding 2nd-order polynomial, i.e.

p2(U) =[

1 VU kU V2U VUkU k2

U

]T. (5)

Furthermore, let φU =[

φU,1 . . . φU,7

]Tdenote the coefficient vector

at U. Now the linear model

PU = p2(U)TφU + εU (6)

can be used to describe the spot price in the close vicinity of U and can

be fitted locally using weighted least squares (WLS), i.e.

φ(U) = argminφU

N

∑i=1

wU(xi)(

Pi − xTi φU

)2(7)

where xi = p2(Ui) and for which a unique closed-form solution exists

provided that the matrix with rows xi corresponding to non-zero weights

has a full rank. The weights are assigned as

wU(xi) = W

(||xi − x||2

h(x)

)(8)

where W(·) is a decreasing weight function taking non-negative argu-

ments. Furthermore, h(x) is the bandwidth used for the particular fit-

ting point, i.e. the maximum euclidean distance between a fitting point

and an observation resulting in a non-zero weight being assigned in

Eq. (7). This implies that a small bandwidth will result in a very flexi-

ble model with low bias and high variance while applying a large band-

width yields a more rigid model having higher bias but lower variance.

9

For readers familiar to exponential smoothing, applying a small band-

width corresponds to having a low level of smoothing in the model. The

bandwidth can therefore be said to be a scalar controlling the rate at

which the weight of an observation, in the estimation, decreases with

distance from the fitting point. From this it follows that the argument

which W(·) takes is the relative distance between the fitting point and

the other point falling within the bandwidth. Following Cleveland and

Devlin (1988) and Nielsen et al. (2000), a tri-cube kernel is chosen as a

weight function so

W(u) =

{(1 − u3)3 u ∈ [0,1)

0 u ∈ [1,∞). (9)

Turning back to the global view on the model, it can be seen that for

an arbitrary chosen U, out of a set of m fitting points, there can be found

a parameter vector φU. From these, the elements of θ(xt) are estimated

as

θ(xt) = θ(p2(U = xt)) = pT2 (U)φ(U) (10)

where φ(U) is the WLS estimate of φU .

The bandwidth, h(x) is chosen so that at any given time 30% of all

observations fulfil ||xi − x||2 ≤ h(x). In other words, the bandwidth is

varied according to the local density of the data by letting h(x) be equal

to the distance of the qth-nearest xi to x, where q is 30% of the total

number of observations (see e.g. Cleveland and Devlin, 1988, for de-

tails). The choice of the criteria that 30% of the observations should fall

within the bandwidth is made since it was desired to obtain as local es-

timates as possible and 30% was the smallest bandwidth that resulted

in a full rank design matrix at all times. This criteria is applied for

estimation in all m = 242 fitting points.

Despite what has been stated previously in this paper regarding

the conditional distribution of the spot prices, using this sort of least

squares technique is deemed suitable for this analysis. This is because

the model is only used for assessing the average dependency between

the variables and for such estimates, Gaussian estimators are gener-

ally known to be the best ones for most types of data. Furthermore, the

non-Gaussianity of the residuals is reduced by the model’s non-linearity.

This aside, as will be demonstrated later on in the paper (Figure 5), de-

spite the prices not being normally distributed, their distribution has

a bell shaped form, making the Gaussian assumption not completely

10

inappropriate. In addition, the analysis is carried out on a very exten-

sive data set containing hourly observations for 22 consecutive months.

Therefore, will the impact of each individual extreme only be minimal.

Hence, the use of robust least squares or similar techniques is not nec-

essary.

How the method is applied in the analysis to follow can be sum-

marised as follows. First the data is scaled so all variables are between

[−1,1]. Then a grid of m = 24 × 24 equidistant fitting points is defined.

For each of these fitting points, Umi, the following steps are taken:

1. Calculate the euclidean distances between every observation and

the fitting point of interest. Applying the bandwidth principle pre-

viously described, these distances are normalised by that corre-

sponding to the qth-nearest neighbour, where q is set to 30%, and

thereby form the input to Eq. (9).

2. Compute the estimate Φ(Umi) of the local polynomial coefficients

at the fitting point Umiby solving Eq. (7).

3. Obtain the local estimate of the spot price at Umifrom Eq. (10)

with p2(Umi) as the polynomial for the particular fitting point as

described by Eq. (5).

The mean spot price for any point U can be obtained by bilinear inter-

polation from the local estimates calculated at each fitting point. This

finally yields a smooth trend surface like those shown and commented

on in the following.

4. General trend: the effect of forecasts on the mean price

On a day-ahead basis, the area spot price is subject to a considerable

uncertainty. It can therefore rightfully be stated that the future spot

price has some unknown distribution and the model presented in the

previous section can be used, if applied correctly, to provide information

about the mean in this distribution.

In Figure 1 the average spot price in DK-1 is estimated as a function

of both the time of the day and the forecasted wind energy production

measured in MWh per hour. From the figure, it is quite obvious that

forecasts of large wind power production in a given hour will, on aver-

age, result in a lower spot price in that hour, since when going along the

wind power-axis, in the increasing direction, the mean price decreases.

11

05

1015

20

0

500

1000

1500

20

40

60

HourForecasted WP production

Pric

e [E

UR

/MW

h]

20

25

30

35

40

45

50

55

Figure 1: The dependence of the spot prices on forecasted wind power production and

its variation throughout the day

During the night, the average price varies from around 30AC/MWh for a

forecasted low wind power production down to around 18AC/MWh for

the hours with forecasted large wind power production. During the

day, this difference between the two extremes in forecasted quantities of

wind power produced is somewhat larger as the prices go from around

50 − 55AC/MWh down to around 30AC/MWh. Due to the infrequent oc-

currence of the installed wind power capacity being fully utilised, the

wind power-axis only reaches 1500 MWh which is somewhat lower than

the full utilisation4. Observations above the 1500 MWh limit are never-

theless used for estimation when it is relevant.

What is also very interesting is that the daily price raise, during

the hours of the day where consumption reaches its daily peak, evens

out as wind power production in the system increases. The reason for

this is that the virtually nil marginal cost of the wind turbines shifts

the supply curve to the right when more wind power is produced and

therefore it takes more consumption to reach the steep end of it. In other

4Installed wind generation capacity in DK-1 was around 2400 MW during the con-

sidered period.

12

words, the increased production of the turbines means that less cost

efficient plants otherwise covering the base load, will be covering the

peaks only. This in turn prevents the even less cost efficient generators

from being utilised during the hours when demand peaks.

As stated earlier, the demand for electricity varies severely through-

out the day and the week. The same quantity of wind power, measured

in MWh, can therefore have quite different effects on the price depend-

ing on the time of the day and the week. More specifically, electricity

demand is generally lower during the evening and the night and there-

fore will a large volume of wind power produced in these hours make up

for a larger share of the total demand than the same quantity would do

during the day. This in turn will cause the equilibrium point of the sup-

ply and demand curves to be placed lower during the evening and the

night than it would during the day. In order to eliminate these effects,

to some extent at least, the wind power forecasts can be included as

the proportional contribution to the total supply instead of its absolute

contribution. In other words, by substituting the forecasted wind power

production, Vt, with the forecasted wind power penetration defined in

Eq. (3), V(p)t , a better prediction of the price equilibrium is gained from

the wind power forecasts.

There are certainly other ways of deriving a number representing

the interaction between wind power predictions and load forecasts. For

instance, the difference between the forecasts could be considered in-

stead of the ratio between the two. Although the relationship will then

appear differently, simulations indicate that the extent of the impact

will be approximately the same. It is also intuitively appealing to work

with values that are between 0 and 1. Therefore, further analysis is

only presented on V(p)t as it is defined in Eq. (3).

In Figure 2 a smooth estimate of the spot price, as a function of

the time of the day and forecasted wind power penetration, is given.

The figure shows the same type of effects as described before. How-

ever, the effects are more dramatic than seen in Figure 1 since the same

actual production now has different effects depending on what time of

the day and the week5 the production occurs. The average spot price

is again considerably lower at times where wind power production has

been predicted to be large. The difference between the two extremes

in forecasted production is roughly the same during night hours, while

5Due to the weekly variation in the load

13

05

1015

20

00.2

0.40.6

20

30

40

50

60

HourForecasted WP penetration

Pric

e [E

UR

/MW

h]

20

25

30

35

40

45

50

55

60

Figure 2: The dependence of the spot prices on forecasted wind power penetration and

its variation throughout the day

the difference has increased during the day. During the day, the average

spot price is around 55− 60AC/MWh when nothing of the demand is sup-

plied by wind power. The average prices then rapidly diminishes with a

small increase in wind power penetration, and after a short stand still

as the penetration approaches 20%, the sharp decline continues up to

around 40% predicted penetration, for which the average spot price is

around 35AC/MWh. When the forecasted wind penetration has reached

40%, a decrease in average price per penetration percent becomes more

subtle and as the forecasted wind power penetration reaches 80%, the

average spot price has declined to around 22 − 25AC/MWh.

Some general information about the characteristics of the supply

function can also be deduced from the figure. The rather sharp gradient

changes in the average price in the lower penetration end of the plot

are a clear indication of the discontinuity of the supply function. Wind

power quickly pushes the steepest end of the supply curve to the right

side of the equilibrium point, and thereby out of the generation port-

folio for that hour, explaining the sharp decline in the average price.

After stabilising itself, the average price decreases rapidly again when

another threshold is pushed out of the equilibrium. The final subtle de-

cline, and the night time behaviour can also be explained by considering

14

<10 11−20 21−30 31−40 41−50 51−60 61−70 >700

10

20

30

40

50P

rice

[EU

R/M

Wh]

Wind penetration [%]

Figure 3: Average spot price, categorised by intervals of forecasted wind power pene-

tration, in DK-1 in the period January 4th 2006 - October 31st 2007

the shape of the underlying supply function, since the equilibrium point

has then reached the flatter part of the supply function where cheaper

energy sources such as Norwegian hydro power and wind power are

placed.

Even though it is clear from Figure 2 that forecasted wind power

does in fact influence the spot prices, it is hard to point out how big the

actual effects are. In Figures 3 and 4 the extent of the effects are better

illustrated. In Figure 3 the average spot price is shown for predicted

wind power penetration on certain intervals in the period which the

data set spans. It shows how the average spot price generally decreases

as the share of wind power in the system increases.

In Figure 4, the impact of forecasted wind power penetration is for-

mulated in terms of reduction in price compared to no wind being present

in the system. For doing this, the assumption is made that wind power

penetration under 4%, corresponding to a production of approximately

80 MWh per hour, has very little or no effects on the spot prices. Obser-

vations falling on this interval are taken as a reference point and rep-

resents the situation when no wind power is predicted to enter the sys-

tem. Comparing the average spot price for the reference group, which

is AC44.43, to that of the remaining observations, where the average is

AC36.68, shows that the spot prices drop on average by 17.5% when the

15

4−10 11−20 21−30 31−40 41−50 51−60 61−70 >700

10

20

30

40

50

60P

rice

redu

ctio

n [%

]

Wind penetration [%]

Figure 4: Reduction in average spot price, compared to the ”no wind” situation, for

different levels of forecasted wind power penetration in DK-1 in the period January 4th

2006 - October 31st 2007

forecasted wind power penetration exceeds 4%. In Figure 4, the pene-

tration levels above 4% have been divided into intervals of 6-10% and

the bars represent how much lower on average, the price is during pe-

riods of the given penetration interval, compared to the reference ”no

wind” situation. The plot clearly illustrates that the spot prices tend to

decrease as the forecasted wind power penetration increases.

The extent and the characteristics of the effects that have been shown

to exist here indicate that properly accounting for them will be of seri-

ous help when electricity spot prices are to be forecasted in an area

penetrated by wind power to some or large extent. These effects are

consistent with what intuitively would be expected and would provide a

forecasting model with vital information about the current shape of the

supply function and thereby a good indication about the equilibrium

point. However although the existence of these effects is undisputed, it

can be debated whether they are for the good or worse, now when the

share of wind power stands to be increased all over the world. Less ex-

pensive electricity might sound appealing for many at first, especially

put in context with marginal bidding. On the other hand, this results in

less contribution to the enormous initial investments of power plants of

any kind. This will in turn reduce investors’ interest in investing in new

16

plants. Furthermore, lower electricity prices pose a threat to the exis-

tence of flexible power plants that produce electricity at high marginal

costs. These plants however contribute heavily to a much needed sta-

bility in the energy supply.

5. Effects of wind power forecasts on price distributional prop-

erties

Having established that forecasted wind power penetration certainly

affects the mean spot price in DK-1, the question remains whether it

affects the distribution of the prices as well. Equipped with more com-

prehensive knowledge about the relationship between price volatility

and one or more of its fundamental causes (in this case wind power

forecasts), one may better explain and hereby estimate future volatility

levels while conditioning it upon these causes, e.g. in a non-parametric

fashion. For carrying out the distribution analysis, the data set is di-

vided into bins, according to forecasted wind power penetration, so that

approximately 2500-3000 observations belong to each segment. Then

the properties of the price distribution are estimated within each bin.

In Figure 5, histograms of the electricity prices are shown for differ-

ent levels of forecasted wind power penetration. The figure illustrates,

what already has been established, that the mean price shifts towards

zero as forecasted wind power penetration increases. Furthermore, the

positive skewness of the price distribution is quite evident from the fig-

ure as well as the fact that the heavy tail diminishes with increased

forecasted wind power penetration. This translates to the statement

that the probability of extremely high prices is much lower when the

wind power penetration is predicted to be high.

The difference in distribution properties is summarised in Table 1.

The first two lines in the table show the shift of mean, already dis-

Table 1: Properties of the spot price distribution for different scenarios of forecasted

wind power penetration

0-5% 5-10% 10-16% 16-25% 25-40% 40-100%

Mean 42.98 41.13 40.26 38.10 33.24 26.02

Std. Dev. 16.95 15.32 14.18 13.08 11.35 11.23

Skewness 0.82 0.48 0.39 0.63 0.32 0.29

Kurtosis 4.41 3.39 3.40 4.05 3.04 4.09

17

0

5

10

Price [EUR]

Pro

port

ion

[%]

0 50 1000

5

10

0 50 100 0 50 100

0−5%5−10%10−16%16−25%25−40%40−100%

0 20 40 60 80 100 1200

2

4

6

8

10

Price [EUR]

Pro

port

ion

[%]

Figure 5: Distribution of prices for different intervals of forecasted wind power pene-

tration

18

cussed, and reduction in standard deviation, indicating less volatility

of the prices. Lines 3 and 4 show how the skewness and kurtosis of

the distributions change for the different levels of penetration. Despite

the fact that no obvious pattern is detectable in lines 3 and 4, they rep-

resent quite dissimilar distributions. Taking the penetration intervals

from left to right in the table, the first distribution is rather skewed

and with high kurtosis, due to the heavy tail seen in Figure 5. Then as

the wind power penetration increases in the 2nd and 3rd intervals, the

tail becomes not as heavy, while the mean does not shift all that much,

explaining the decrease in both skewness and kurtosis. When the pene-

tration reaches the level of the 4th interval, the mean has shifted more

while the rather high prices still occur. Hence, the increase in skewness

and kurtosis. For predicted wind power penetration between 25-40%

these extreme price situations no longer occur, reflected in a decrease

both in skewness and kurtosis. This threshold effect is yet another non-

linear effect introduced in the market by wind power or wind power

forecasts. Finally, for the highest forecasted penetration interval, the

frequency of very low prices increases substantially, explaining the re-

duction of skewness and increase in kurtosis. So to summarise, going

from a low wind power penetration to high, generally leads to a lower

skewness due to the diminishing frequency of very high prices along

with the increased probability of very low prices.

Another thing that catches the eye in Figure 5 is the relatively high

proportion of prices equal to zero in the histogram representing the

highest penetration interval. Over 2% of the times when wind pene-

tration is above 40%, electricity spot prices are 0AC/MWh. Although

ill-detectable from the figure, this situation rarely occurs for the 25 -

40% penetration interval, while it does not occur for the lower levels of

penetration. For the four lower ones, the minimum price does however

approach zero as the forecasted penetration increases. The occurrence

of the spot price being 0AC/MWh will result in a negative cash flow for

producers subject to imbalance costs in that hour. In other words, it

will pay off, even for producers with no marginal production costs, not

to produce electricity. This further supports what was stated at the end

of previous section about the down side of increased wind power pene-

tration under current market conditions.

From a modelling perspective, the dissimilarity of the spot price

distribution between different levels of forecasted wind power penetra-

tion strongly indicates that estimating prediction intervals conditioned

on the wind power predictions is worth the effort. It is quite obvious

19

that the spot prices are not Gaussian distributed and therefore it must

be deemed highly unlikely that models constructed with least squares

techniques will have Gaussian residuals. Prediction intervals for such

models should therefore be estimated using other techniques. In fact

the distributions are so far from parameterised distributions that it

seems reasonable to conclude that non-parametric approaches, like for

instance quantile regression (Møller et al., 2008), will return the most

reliable prediction intervals.

6. Conclusions and Discussion

The analysis presented in this paper demonstrates the dramatic im-

pact of predicted wind power penetration in the system on not only the

level of the spot prices but also their distributional characteristics. The

spot price is, on average, shown to decrease with increased predicted

wind power penetration, while intra-day price variations diminish to

some extent. As all this happens in a non-linear manner, the use of the

non-parametric regression model for the analysis proves to be very ben-

eficial. Furthermore, wind power forecasts are shown to cause threshold

effect in the price behaviour, with e.g. the appearance of zero prices, or

the removal of extreme prices. They could therefore contribute to an

understanding of some of the non-linearities and regime-switching be-

haviour in the prices. The results of this paper therefore support some

of the conclusions of Karakatsani and Bunn (2008) such that aspects

of plant dynamics should be considered when models of the short-term

dynamics of electricity spot prices are to be derived. It would therefore

be interesting to derive a forecasting model for these prices that ac-

counts for the impact of forecasted wind-to-load ratio (see e.g. Jonsson,

2008). When developing such an approach, accounting for the uncov-

ered non-linearities in the relationship between forecasted wind power

penetration and day-ahead electricity prices will be essential.

The findings of this paper confirm what previous studies of the im-

pact of wind power on electricity spot prices have shown, that wind

power has a non-negligible impact on day-ahead electricity prices. Here

however, based on the claim that it is instead the predicted wind power

penetration that should be seen as an explanatory variable, the impact

is shown to be more substantial than previously recorded (Enevoldson

et al., 2006; Moesgaard and Morthorst, 2008). The corresponding rela-

tionship moreover turns out to be highly non-linear, and the distribu-

tional characteristics of prices are also affected. The results also show

20

that a simple assumption like Gaussianity commonly made for the es-

timation of prediction intervals of electricity prices (e.g. Nogales and

Conejo, 2006) does not hold. The fact that the spot prices themselves

are so far from being Normally distributed will certainly be reflected in

the residual distribution of a forecasting model, which parameters are

estimated with a least squares criteria. Furthermore, as the price dis-

tribution has also been shown to be dependent on an external signal,

prediction intervals should be generated accounting for this relation,

thus yielding conditional prediction intervals. The analysis therefore

indicates that estimating the uncertainty conditioned on an explana-

tory variable, e.g. wind power forecasts, in a non-parametric fashion

could increase the resolution of probabilistic forecasts of electricity spot

prices.

In this paper, the scope has been the Western Danish price area (DK-

1) at Nord Pool. This price area may be seen as representative of the

future deregulated electricity with significant penetration of renewable

energy generation. Although the share of wind power in DK-1 is larger

than anywhere else in the world, it is very plausible that the effects,

revealed here, can also be detected in other market areas as well, pen-

etrated by wind power to some extent — for instance in Spain or Ger-

many. Similar causes would have similar effects, the principal ones

being varying availability of the fuel and extremely low marginal costs.

The severe impact of wind power forecasts on all behaviour of the

electricity prices is also interesting to consider in the context of market

design and with the long-term development of the production portfolio

in Denmark in mind — where the intention is to increase the share

of wind power generation up to 50% of the electricity consumption by

2025 (Ea Energy Analyses, 2007). With the current market structure

of marginal bidding, the frequency of hours where the spot price is

zero is bound to increase along with growing wind power penetration

in the system in a similar manner as has been demonstrated here. This

will further enhance the stochastic threshold effect demonstrated here,

and thereby increase price volatility and cause it to have alternating

weather dependent patterns (Meibom, 2007). This aside, higher risk

premium will be required on investments in all sorts of new energy

generation capacity and investment in conventional power generation

capacity will be more focused on flexibility than efficiency since those

plants will have to rely more on the increased demand on the balance

markets as a source of income (Meibom, 2007). The impact of wind

power on the price making at the electricity markets should therefore

21

be given careful thought when the possibility of increasing the share

of wind power, and non-dispatchable energy sources in general, in the

generation portfolio is discussed. Especially, the fact that wind power

penetration has some non-linear effects on the prices should be taken

into consideration, as it implies that current market situation can not

be scaled directly for analysing the future circumstances. In the con-

text of market design, it will also be interesting to monitor the market’s

response to other renewable sources reaching the status of making up

for a significant share of the energy supply. Those sources in all likeli-

hood being solar or wave energy in the medium term. Whether this will

level out the effect of increased wind power or magnify them will play

an important role in future development of the market structure.

7. Acknowledgements

The authors would like to thank Energinet.dk, the danish Trans-

mission system operator, and Nord Pool ASA for providing data for

the analysis, publicly available at http://www.energinet.dk/en/menu/Market/Market.htm and at http://www.nordpoolspot.com .

Authors are also grateful to Henrik Aa. Nielsen at ENFOR A/S for fruit-

ful discussions and useful comments and Torben Skov Nielsen at EN-

FOR A/S for providing wind power predictions.

References

Bathurst, G. N., Weatherill, J., Strabac, G., 2002. Trading wind gen-

eration in short term energy markets. IEEE Transactions on Power

Systems 17(3), 782–89.

Boogert, A., Dupont, D., 2005. On the effectiveness of the anti-gaming

policy between the day-ahead and real-time electricity markets in the

netherlands. Energy Economics 27(5), 752–770.

Christensen, B. J., Jensen, T. E., Mølgaard, R., 2007. Market power

in power markets: Evidence from forward prices of electricity. CRE-

ATES Research Paper No. 2007-30. Available at http://ssrn.com/abstract=1150145 .

Cleveland, W. S., Devlin, S. J., 1988. Locally weighted regression: An

approach to regression analysis by local fitting. Journal of the Ameri-

can Statistical Association 83(403), 596–610.

22

Conejo, A. J., Contreras, J., Espınola, R., Plazas, M. A., 2005. Forecast-

ing electricity prices for a day-ahead pool-based electric energy mar-

ket. International Journal of Forecasting 21(3), 435–462.

Costa, A., Crespo, A., Navarro, J., Lizcano, G., Madsen, H., Feitona,

E., 2008. A review on the young history of wind power short-term

prediction. Renewable & Sustainable Energy Reviews 12(6), 1725–

1744.

Cuaresma, J. C., Hlouskova, J., Kossmeier, S., Obersteiner, M., 2004.

Forecasting electricity spot-prices using linear univariate time-series

models. Applied Energy 77(1), 87–106.

Daneshi, H., Daneshi, A., April 2008. Price forecasting in deregulated

electricity markets - a bibliographical survey. In: The 3rd IEEE Inter-

national Conference on Electric Utility Deregulation, Restructuring,

and Power Technology (DRPT2008). Nanjing, China.

Ea Energy Analyses, 2007. 50% wind power in denmark in 2025 -

english summary. Available at: http://www.talentfactory.dk/media(2513,1033)/081029_50pct._wind_power_i%n_dk_in _2025.pdf .

Eggertsson, H., 2003. The scandinavian elecricity power market and

market power. Master’s thesis, Technical University of Denmark,

DTU, Kgs. Lyngby, Denmark, available at http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=2533 .

Enevoldson, S. W., Østergaard, P. A., Morthorst, P. E., Moesgaard, R.,

2006. Vindkraftens betydning for elprisen i danmark. Tech. rep., IBT-

Wind, in Danish.

Giabardo, P., Zugno, M., 2008. Competitive bidding and stability anal-

ysis in electricity markets using control theory. Master’s thesis, In-

formatics and Mathematical Modeling, Technical University of Den-

mark, DTU, Kgs. Lyngby, Denmark, available at www2.imm.dtu.dk/˜pp/thesis.htm .

Giabardo, P., Zugno, M., Pinson, P., Madsen, H., 2009. Feedback, com-

petition and stochasticity in a day ahead electricity market. Energy

Economics Available online.

23

Giebel, G., Kariniotakis, G., Brownsword, R., 2003. The state-

of-the-art in short-term prediction of wind power - a litera-

ture overview. EU project Anemos, Deliverable Report D1.1,

Available at http://anemos.cma.fr/download/ANEMOS_D1.1_StateOfTheArt_v1.1.pdf .

Gonzalez, A. M., Roque, A. M. S., Garcıa-Gonzalez, J., 2005. Modeling

and forecasting electricity prices with input/output hidden markov

models. IEEE Transactions on Power Systems 20(1), 13–24.

Huisman, R., Huurman, C., Mahieu, R., 2006. Hourly electricity prices

in day-ahead markets. Energy Economics 29(2), 240–248.

Jonsson, T., 2008. Forecasting of electricity prices accounting for wind

power predictions. Master’s thesis, Informatics and Mathematical

Modeling, Technical University of Denmark, DTU, Kgs. Lyngby, Den-

mark.

Karakatsani, N. V., Bunn, D. W., 2008. Forecasting electricity prices:

The impact of fundamentals and time-varying coefficients. Interna-

tional Journal of Forecasting 24(4), 764–785.

Kosater, P., Mosler, K., 2006. Can Markov regime-switching models

improve power-price forecasts? Evidence from German daily power

prices. Applied Energy 83(9), 943–958.

Longstaff, F. A., Wang, A. W., 2004. Electricity forward prices: A high-

frequency empirical analysis. The Journal of Finance 59(4), 1877–

1900.

Madsen, H., Holst, J., 2000. Modelling Non-Linear and Non-Stationary

Time Series (Lecture Notes). IMM, DTU, Kgs. Lyngby, Denmark.

Mandal, P., Senjyu, T., Funabashi, T., 2006. Neural networks approach

to forecast several hour ahead electricity prices and loads in deregu-

lated markets. Energy Conversion & Management 47(15-16), 2128–

2142.

Matevosyan, J., Soder, L., 2006. Minimization of imbalance cost trading

wind power on the short-term power market. IEEE Transactions on

Power Systems 21(3), 1396–1404.

Meibom, P., 2007. Market consequences [in my view]. IEEE Power and

Energy Magazine 5(6), 120–118.

24

Moesgaard, R., Morthorst, P. E., April 2008. The impact of wind power

on electricity prices in denmark. In: EWEC 2008, European Wind

Energy Conference, Business and Policy Track. Brussels, Belgium.

Møller, J. K., Nielsen, H. A., Madsen, H., 2008. Time-adaptive quantile

regression. Computational Statistics and Data Analysis 52(3), 1292–

1303.

Morthorst, P. E., 2003. Wind power and the conditions at a liberalized

power market. Wind Energy 6(3), 297–308.

Nielsen, H. A., Nielsen, T. S., Joensen, A. K., Madsen, H., Holst, J., 2000.

Tracking time-varying coefficient functions. International Journal of

Adaptive Control and Signal Processing 14(8), 813–828.

Nielsen, T. S., Nielsen, H. A., Madsen, H., 2002. Prediction of wind

power using time-varying coefficient functions. In: 15th IFAC World

Congress. Barcelona, Spain.

Nogales, F., Conejo, A. J., 2006. Electricity price forecasting through

transfer function models. Journal of Operational Research Society

57(3), 350–356.

Nord Pool Spot AS, 2006a. Bidding in Nord Pool Spot’s Elspot Market.

Available at www.nordpoolspot.com .

Nord Pool Spot AS, 2006b. Calculation of System- and Area prices.

Available at www.nordpoolspot.com .

Panagiotelis, A., Smith, M., 2008. Bayesian density forecasting of intra-

day electricity prices using multivariate skew t distributions. Inter-

national Journal of Forecasting 24(4), 710–727.

Pinson, P., Chevallier, C., Kariniotakis, G. N., 2007. Trading wind gen-

eration from short-term probabilistic forecasts of wind power. IEEE

Transactions on Power Systems 22 (3), 1148–1156.

Ruibal, C. M., Mazumdar, M., 2008. Forecasting the mean and the vari-

ance of electricity prices in deregulated markets. IEEE Transactions

on Power Systems 23 (1), 25–32.

Schwarz, H.-G., Lang, C., Meier, S., 2007. Market power in the german

wholesale electricity market: What are the political options? Avail-

able at SSRN, http://ssrn.com/abstract=1028201 .

25

Sewalt, M., de Jong, C., 2003. Negative prices in electricity markets.

Commodities Now. Available at http://www.erasmusenergy.com/articles/91/1/Negative-prices-in-electrici%ty-markets/Page1.html .

Skytte, K., 1999. The regulating power market on the nordic power ex-

change nord pool: an econometric analysis. Energy Economics 21(4),

295–308.

Taylor, J. W., McSharry, P. E., 2007. Short-term load forecasting meth-

ods: An evaluation based on european data. IEEE Transactions on

Power Systems 22(4), 2213–2219.

Vehvilainen, I., Pyykkonen, T., 2005. Stochastic factor model for elec-

tricity spot price - the case of the nordic market. Energy Economics

27(2), 351–367.

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